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November 6th, 2017, 11:50 AM   #1
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I need help for a probability question

Let A, B be two events in a probability space. The probability
that A happens is 1/2 The probability that B happens is 1/2
The probability that none of the events happen is 1/2

Compute the conditional probability P[A | B]. Are A and B independent?
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November 6th, 2017, 01:38 PM   #2
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If they were independent the probability of none happening is 1/4=(1-P(A))(1-P(B)), so they are not independent.

P(A or B)=1-P(none)=1/2
P(A or B)=P(A)+P(B)-P(A and B)
Therefore P(A and B)=1/2 leading to P(A|B)=1.
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